Spectral Efficiency Considerations for Packet Radio
Phil Karn, KA9Q
Radio spectrum is a lot like land; with the possible
exception of the Dutch, nobody’s making any more of it.
So the enormous growth in demand for spectrum means
that existing users, especially radio amateurs, either
have to find ways to make do with less, be displaced by
new users considered more worthy by regulatory
agencies, or both.This paper qualitatively discusses
the spectral efficiency of packet radio from several
angles, ranging from antenna design, RF modulation and
channel access methods to network protocols, routing
algorithms and data encoding methods. Maximizing the
useful carrying capacity of a spectrum assignment
requires a comprehensive look at all of these factors
and more. Digital techniques finally make it possible
to exploit these gains, but so far amateur radio has
been very slow in adopting them. I hope that this paper
will stimulate some work in this direction.
Measuring Spectral Efficiency
One seemingly basic problem with spectral efficiency is this:
How do you measure it? For example, in the debate over the
codeless license, CW was frequently asserted to be more
efficient than all other operating modes because it (usually)
uses less bandwidth. In effect, the units for measuring
spectral efficiency were claimed to be 1/Hz; the narrower the
signal, the better. But this is a naive measure of efficiency
because it doesn’t take into account the rate at which
information is being transmitted. A better measure is the ratio
of the data rate to the occupied bandwidth; this has units of
“bits per second per Hz of bandwidth”. Modems are frequently
evaluated in this way; indeed, the FCC sets minimum
requirements for this figure for commercial digital microwave
systems.
Unfortunately, even this figure does not give the complete
picture. Very few (if any) individual radio transmitters have
exclusive, worldwide use of their channels. Somewhere else that
same spectrum is almost certainly in use by other transmitters,
and hopefully they are all far enough away from each other to
avoid mutual interference. This is commonly known as
“geographic spectrum reuse”. A combination of directional
antennas and/or physical separation (terrain blocking or
propagation losses) isolates the transmitters in different
geographic areas to avoid harmful interference between them.
So a better measure of spectrum efficiency would have units of
Sbits per second per Hz of occupied bandwidth per square
kilometer”. This is the total useful data rate, summed across
all of the transmitters in a given geographic area that are
sharing a given piece of spectrum.
Yet another factor that we should take into account is the
distance involved. Just as the work performed by a freight
company is the product of cargo weight times the distance it is
moved, the measure of useful “work” performed by a data network
should be bits times distance.
This prevents any apples-and-oranges comparisons of spectral
efficiency between wide- and local-area networks. So our final
measure of network spectral efficiency has units of “bits per
second times distance moved, per Hz of occupied bandwidth, per
square kilometer of geographic area”:
where:
E = network spectrum efficiency figure of merit
r = total network traffic capacity in bits/sec
D = average distance between source and destination nodes in km
B = total RF bandwidth allocated to the network in Hz
A = geographical area occupied by the RF allocation in square
km
The value E is the figure that we should maximize.
Directional Antennas
One effective way to increase the carrying capacity of spectrum
is by using highly directional antennas, especially on the
higher UHF and microwave bands. Glenn Elmore, N6GN, has made
this point quite eloquently. [Elmore90] I completely agree with
Glenn that amateurs should deploy microwave links with
directional antennas whenever and wherever they are practical.
Because microwave antenna patterns can be made so narrow, the
design of the associated modem hardly matters (as long as it
works). Even with a “low efficiency” modem (in a bits/sec/Hz
sense), the resulting system spectral efficiency is still far
larger than on VHF with omnidirectional antennas because so
little geographic area is covered by each microwave beam. This
allows many different links to share the same spectrum in very
close proximity without interference.
However, there are still many situations where point-to-point
microwave links are not yet practical, such as portable and
mobile stations (particularly in emergency situations), and
where line-of-sight microwave propagation is obstructed (e.g.,
by trees and hills). So VHF and UHF packet radio with
conventional low-gain antennas will still be with us for quite
some time, and the resulting interference problems must still
be dealt with.
Interference Limited Systems
This brings up a vitally important issue in the calculation of
spectral efficiency that is only now getting the attention it
deserves. The single most important factor in the efficient use
of spectrum is the minimum geographic spacing required to avoid
harmful co-channel interference between transmitters. The
closer the allowable co-channel transmitter spacing, the more
traffic the channel can support in a given geographic region.
When spectrum is “reused” in this manner, it is not necessary
that there be no interference (i.e., that any co-channel
interference be well below the noise floor of the receivers).
It is only necessary that a desired signal be sufficiently
stronger than the undesired signals at a given receiver so that
the demodulator can work properly even in the presence of this
weak interference. This is referred to as operating in an
“interference limited” (as opposed to “noise limited”)
environment.
Unfortunately, many amateur repeater owners insist on a very
wide protection area for their frequency assignment to preclude
the accidental triggering of their systems by the weak, distant
users of other repeaters sharing the same assignment. They
refuse to implement tone-coded squelch (PL) even when it could
totally solve the problem because of the advantage given to
local users by the FM capture effect. As we will see, this
attitude is extremely wasteful of spectrum.
The interference rejection capability (aka “capture effect”) of
the modulation method in use therefore becomes a prime factor
in the efficiency calculations. However, low (good) “capture
ratios” are inherently associated with wide band modulation
methods, while narrow band modulation schemes are inherently
much more sensitive to interference. Yet low capture ratios are
so vital to spectral efficiency that they almost always “pay
back” far more than they cost in extra bandwidth by allowing
much closer co-channel transmitter spacing. This leads to the
somewhat paradoxical fact that by going to a wider (and
seemingly less efficient) modulation method, overall spectrum
efficiency can often be greatly increased! [Costas59] This is
why, for example, current cellular telephone systems use FM
rather than SSB; FM has a capture effect while SSB does not, so
using FM more readily allows the reuse of frequencies in other
nearby cells. The bottom line is that a FM cellular radio
system is more spectrally efficient than one using SSB, despite
the much wider FM channel.
It is most unfortunate that the FCC did not understand this
paradoxical connection between modulation bandwidth and
spectrum efficiency when they were convinced to reallocate 220-
222 MHz to the Land Mobile Service for use with a supposedly
more efficient modulation method, SSB. [Lee89] gives this
approximate formula for the frequency reuse factor as a
function of the required carrier-to-interference ratio in a
hexagonal cellular radio system that uses omnidirectional
antennas:
where
K = frequency reuse factor.
C/I = required carrier-to-interference ratio (expressed as a
power ratio, not dB)
š = propagation slope factor, 2 for free space (inverse square),
4 for a typical terrestrial mobile environment
A given channel can be used in only 1/K of the cells. E.g., if
C over I is 18 dB (as it is in a FM cellular radio system),
then K = 7 and a given channel can be used in only 1 of every 7
cells.
If the required C over I ratio can be decreased to 10 dB, then
K would be less than 3; this would more than double the number
of transmitters that could share each channel.
The next generation of cellular telephony will substantially
improve on FM’s capacity by going digital, where by the proper
choice of modulation method and with forward error correction
coding (FEC), the capture ratio can be as low as 7 dB. The most
promising scheme, not coincidentally, also has the widest
signal bandwidth: CDMA (Code Division Multiple Access, more
commonly known as “spread spectrum”). [Gilhousen91]
The big win of spread spectrum for mobile communications is its
ability to handle multipath fading. In analog FM, 8 dB of
system margin is required to account for fading, over and above
the 10 dB C/I ratio required on a nonfading channel. But spread
spectrum allows the separation of multipath components,
avoiding the rapid “mobile flutter” so characteristic of
multipath fading in narrow band FM. Automatic power control
easily compensates for the slow propagation variations that
remain. This avoids the need for a big fading margin and allows
co-channel transmitters to be much more closely spaced. In a
network of fixed stations, multipath fading is not as much of a
problem, so the important factor in system capacity
calculations is just the C/I ratio required by the modulation
(and coding method, if any). In both the fixed and mobile
cases, the extra bandwidth required by adding FEC usually more
than pays for itself in the closer co-channel transmitter
spacing it allows.
Power Control and Routing
Simply using RF modems capable of good capture ratios isn’t
enough, however; automatic transmitter power control is also
required to take full advantage of them. With automatic power
control, each transmitter ensures, on a continuous basis, that
a sufficient signal-to-noise ratio (actually E sub b over N sub
0 ratio) exists at its intended receiver and no more. Running
more power than necessary to yield good performance is like
buying higher octane gasoline than your car needs—it doesn’t
work any better, and you only squander money and natural
resources. The whole purpose of designing modems with good
capture ratios is to allow transmitters sharing the same
channel to be placed more closely together, and this is not
possible unless each transmitter uses only the minimum power
required to reach any given receiver. The transmitter power
required to reach a given receiver in a network of packet
stations can vary widely depending on the distance between
them, the presence of obstacles, nonideal antenna patterns,
etc. So an interesting question appears: given the choice of
relaying a packet to one of two intermediate stations between
the sender and the destination, one of which is close and the
other farther away (but closer to the destination), which one
should be chosen? The answer? It depends. If the packet must be
delivered with the absolute minimum delay, then sending the
packet to the relay station that is farther away (and that much
closer to the destination) will clearly get it there faster,
since each relay hop takes time. But the additional transmitter
power required to reach the station farther away means that a
larger geographical area must be blanketed by the transmission,
thus denying the simultaneous reuse of the channel to that many
more stations. So if maximizing total network capacity is the
goal, then the routing algorithm must minimize something other
than simply the number of hops taken (or even the total
distance traveled) to reach a destination.
Dave Mills, W3HCF has reported on a study of this problem done
for the DARPA Multiple Satellite System (MSS). [Mills87] The
study concluded that the proper metric to be minimized by an
MSS routing algorithm is the sum of the squares of the
distances between the nodes (relay satellites). Because of the
inverse-square law in free-space radio propagation, this
effectively minimizes the total RF energy, summed over all of
the transmitters involved, needed to relay a bit of information
to its destination. This is true even when more nodes are used
than if the routing algorithm simply picked the least number of
hops to the destination.
In a terrestrial store-and-forward network, propagation losses
usually increase with distance much faster than the square of
the distance because of obstructions, scattering and multipath;
the fourth power of the distance is generally used in analysis.
But if each node measures the actual transmitter power required
to reach a given destination and reports that as its routing
metric for that link, then the propagation effects are
automatically taken into account when the routing algorithm
minimizes the sum of the transmitter powers used in reaching a
given destination.
This tradeoff between delay and network efficiency suggests an
interesting use for the long-ignored type-of-service (TOS) bits
in the IP header. By default, packets would be routed using the
minimum-total-power criteria, but IP datagrams that have the
“low delay” bit set would use a different set of routing
criteria that minimize delay at the expense of network
capacity. This could be quite useful for emergency or priority
traffic.
Channel Access Methods
The algorithms that determine when a station transmits are
another important factor in a network’s overall spectral
efficiency. Because of the need to operate in an interference-
limited environment, carrier-sense multiple access (CSMA)
schemes won’t work very well if they always inhibit
transmission whenever a signal is heard on channel, no matter
how far away that other transmitter may be. Such systems are
analogous to the repeater operator who refuses to use PL and
still complains about remote triggering of his repeater, as
mentioned in an earlier footnote. Schemes that rely on
receiver feedback (as opposed to channel sensing at the
transmitter) to avoid collisions would seem to be the only
practical approach to this problem. See [Karn90] for a
discussion of one possible approach.
Protocols
From the point of view of the packet subnetwork designer, the
upper layer protocols used are irrelevant; they are simply part
of the user data that is to be moved. However, from the user’s
point of view, everything but his data is overhead. Therefore
the cost of these protocols could be considered as part of the
overall network spectral efficiency equation.
When properly implemented and tuned, the overhead taken by the
protocols used in a computer network is usually a second-order
factor in the overall efficiency of the system. Even the
overhead of a “heavy” protocol like TCP/IP is easily minimized
by using sufficiently large data packet sizes or by compressing
headers [Jacobson90].
But this applies only when the protocols are used as intended,
e.g., providing reliable point-to-point transfers with TCP.
Unfortunately, it is a common practice to use multiple point-to-
point protocol connections to emulate a broadcast or multicast
service; the data is sent N times to N receivers, even when
omnidirectional antennas are being used and the receivers could
easily have shared a common, single transmission. The biggest
offender in this regard is the DX Cluster, which in this
author’s opinion comes close to being a criminal abuse of the
AX.25 protocol. Another is the common practice of multiple
users individually re-reading the same public bulletin from a
BBS when the bulletin could have been broadcast to everyone at
once. Fortunately, protocols designed specifically for the
efficient broadcast of digital information have been designed
and are now being deployed. [Price90] Given that much of the
information carried by the amateur packet radio network is of
general interest, such protocols should significantly enhance
the effective capacity of the network. In our network
efficiency equation, a broadcast protocol in use by N receivers
would effectively multiply overall efficiency by approximately
N.
Compression
Another higher-level issue in spectrum efficiency is the use of
data compression. A network doesn’t care about the values of
the bits it carries; it “costs” just as much to send a million
“0” bits as a million-bit text document, even though the useful
information content of the former is probably quite a bit less.
Users should therefore try to use the network’s capacity in the
most efficient way possible by compressing their data before
transmission.
Data compression has been well studied and is widely used in
the computer field. Public domain and shareware utilities (such
as PKZIP) are quite common, and they typically yield 50-80%
reductions in the size of English text and computer program
files. Users can run these utilities manually before sending
their files over the network, or they could use the automatic
LZW stream compression features built into the NOS TCP/IP
package by Anders Klemets. [Klemets91] Data compression does
not increase the capacity of the network per se, it simply uses
it more efficiently. But the bottom line is the same: the
network can do more useful work (moving user data) with the
same spectrum resources.
Conclusion
It is the author’s belief that an efficient, self-configuring,
single-channel half-duplex store-and-forward amateur packet
radio network would be quite practical if the design principles
discussed here were pursued.
The much-maligned “digipeater network” is so bad only because
the modulation methods, channel access and routing algorithms
are all so sub-optimal, and because there is no power control
at all. Properly designed, a collection of “digipeaters done
right” would have a lot of practical advantages because of its
decentralized nature. All the nodes would be equal, so the
failure of any one node need not bring the entire network down,
as would happen if the hub or repeater in a centralized network
were to fail. (This network model was used for the original
DARPA packet radio experiments precisely because of this
inherent robustness.)
And the system capacity could actually increase as additional
nodes were added, because the average inter-nodal distance
would decrease, allowing the min-power routing and automatic
power control algorithms to reduce average transmitter powers.
As a first step toward such a network, I urge the manufacturers
of digital radios to include the “hooks” for automatic power
control. What’s urgently needed is a way for the packet
controller CPU to quickly vary the power of the transmitter in
discrete steps, e.g., with a D/A converter, and a way to
measure incoming receiver signal levels, e.g., with an A/D
converter on the AGC line. Once we have these hardware
features, we software types can do the rest.
Acknowledgements
I would like to thank my new colleagues at Qualcomm, Inc,
particularly Klein Gilhousen, WT6G and Mike Brock, WB6HHV, for
some very enlightening discussions.
References
[Costas59] John P. Costas, K2EN, Poisson, Shannon and the Radio
Amateur, Proceedings of the IRE, December 1959.
[Elmore90] Glenn Elmore, N6GN, Physical Layer Considerations in
Building
a High Speed Amateur Radio Network, ARRL Computer Networking
Conference, 1990.
[Gilhousen91] Klein S. Gilhousen, WT6G, et al, On the Capacity
of a Cellular CDMA System, IEEE Transactions on Vehicular
Technology, Vol. 40 No. 2, May 1991.
[Jacobson90] Van Jacobson, Compressing TCP/IP Headers for Low-
Speed Serial
Links, Internet RFC 1144, February 1990.
[Karn90] Phil Karn, KA9Q, MACA - A New Channel Access Method
for Packet Radio, ARRL Computer Networking Conference,
September 1990.
[Klemets91] Anders Klemets, SM0RGV, LZW Compression of
InteractiveNetwork Traffic, ARRL Computer Networking
Conference, 1991.
[Lee89] William C. Y. Lee, Mobile Cellular Telecommunication
Systems, McGraw-Hill, 1989.
[Lee91] William C. Y. Lee, Overview of Cellular CDMA, IEEE
Transactions on Vehicular Technology, Vol. 40 No. 2, May 1991.
[Mills87] David L. Mills, W3HCF, Advanced Topics on the DARPA
Internet System, Interop ‘88 tutorial notes, September 1988.
[Price90] Harold Price, NK6K, and Geoff Ward, K8KA, Pacsat
Broadcast Protocol, ARRL Computer Networking Conference,
September 1990. (See also other related papers in the same
issue).